Spin-orbit coupling and $g$-factor of $X$-valley in cubic GaN

We report our theoretically investigation on the spin-orbit coupling and $g$-factor of the $X$-valley in cubic GaN. We find that the spin-orbit coupling coefficient from $sp^3d^5s^\ast$ tight-binding model is 0.029\,eV$\cdot$Å, which is comparable with that in cubic GaAs. By employing the ${\bf k}\cdot{\bf p}$ theory, we find that the $g$-factor in this case is only slightly different from the free electron $g$-factor. These results are expected to be important for the on-going study on spin dynamics far away from equilibrium in cubic GaN.

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